Gel'fand inverse problem for a quadratic operator pencil

2006-02-16T15:15:12Z (GMT) by Y.V. Kurylev M. Lassas
In this paper we consider the inverse boundary value problem for the operator pencil A(lambda) = a(x, D)-i lambda b(0)(x)-lambda(2) where a(x, D) is an elliptic second-order operator on a differentiable manifold M with boundary. The manifold M can be interpreted as a Riemannian manifold (M, g) where g is the metric generated by a(x, D). We assume that the Gel'fand data on the boundary is given; i.e., we know the boundary partial derivative M and the boundary values of the fundamental solution of A(lambda), namely, R-lambda(x, y), x, y is an element of partial derivative M, lambda is an element of C. We show that if (M, g) satisfies some geometric condition then the Gel'fand data determine the manifold M, the metric g, the coefficient b(0)(s) uniquely and also the equivalence class of a(x, D) with respect to the group of generalized gauge transformations.